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          题解：P1079 [NOIP2012 提高组] Vigenère 密码
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              <time title="创建时间：2025-04-30 20:42:54 / 修改时间：22:16:07" itemprop="dateCreated datePublished" datetime="2025-04-30T20:42:54+08:00">2025-04-30</time>
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        <h1 id="P1079-题解"><a href="#P1079-题解" class="headerlink" title="P1079 题解"></a><a target="_blank" rel="noopener" href="https://www.luogu.com.cn/problem/P1079">P1079 题解</a></h1><p>本蒟蒻的第一篇题解。</p>
<h2 id="大体思路："><a href="#大体思路：" class="headerlink" title="大体思路："></a>大体思路：</h2><p>先定义一个密钥 $k$ 的指针变量 $q$，表示密文要减去 $k$ 的第几位。</p>
<p>定义指针变量 $i$，表示密文 $M$ 的第几位。从 $0$ 到 $|M|$（注：$|M|$ 表示 $M$ 的长度。）枚举 $i$，判断 $M_i$ 的大小写，再判断密钥 $k_q$ 的大小写：</p>
<ul>
<li><p>如果 $k_q$ 为大写，则遍历 $k_q - \texttt A$ 次；</p>
</li>
<li><p>反之，遍历 $k_q - \texttt a$ 次。</p>
</li>
</ul>
<p>在每一次遍历中，$M_i$ 减去 $1$，且：</p>
<ul>
<li><p>如果 $M_i$ 为大写且 $M_i &lt; \texttt A$ 时，$M_i \gets \texttt Z$；</p>
</li>
<li><p>如果 $M_i$ 为小写且 $M_i &lt; \texttt a$ 时，$M_i \gets \texttt z$。</p>
</li>
</ul>
<p>遍历完之后，变量 $q$ 增加 $1$，如果 $q=|k|$，则 $q \gets 0$。</p>
<p>这样就可以把密文转化为明文。</p>
<h2 id="示范代码："><a href="#示范代码：" class="headerlink" title="示范代码："></a>示范代码：</h2><figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line">string k,s;<span class="comment">//定义密钥字符串k和密文字符串s</span></span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span> </span>&#123;</span><br><span class="line"></span><br><span class="line">    cin&gt;&gt;k&gt;&gt;s;<span class="comment">//输入k和s</span></span><br><span class="line"></span><br><span class="line">    <span class="type">int</span> q=<span class="number">0</span>;<span class="comment">//定义指针变量q</span></span><br><span class="line"></span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">0</span>;i&lt;s.<span class="built_in">size</span>();i++)&#123;<span class="comment">//遍历密文字符串</span></span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span>(s[i]&gt;=<span class="string">&#x27;A&#x27;</span>&amp;&amp;s[i]&lt;=<span class="string">&#x27;Z&#x27;</span>)&#123;<span class="comment">//判断密文大小写</span></span><br><span class="line"></span><br><span class="line">            <span class="type">int</span> h=k[q]&gt;=<span class="string">&#x27;A&#x27;</span>&amp;&amp;k[q]&lt;=<span class="string">&#x27;Z&#x27;</span>?k[q]-<span class="string">&#x27;A&#x27;</span>:k[q]-<span class="string">&#x27;a&#x27;</span>;<span class="comment">//判断密钥大小写，并求出遍历次数</span></span><br><span class="line"></span><br><span class="line">            <span class="keyword">for</span>(<span class="type">int</span> j=<span class="number">0</span>;j&lt;h;j++)&#123;<span class="comment">//遍历还原</span></span><br><span class="line"></span><br><span class="line">                s[i]--;</span><br><span class="line"></span><br><span class="line">                <span class="keyword">if</span>(s[i]&lt;<span class="string">&#x27;A&#x27;</span>)&#123;<span class="comment">//特判，使变化符合规则</span></span><br><span class="line"></span><br><span class="line">                    s[i]=<span class="string">&#x27;Z&#x27;</span>;</span><br><span class="line"></span><br><span class="line">                &#125;</span><br><span class="line"></span><br><span class="line">            &#125;</span><br><span class="line"></span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span>(s[i]&gt;=<span class="string">&#x27;a&#x27;</span>&amp;&amp;s[i]&lt;=<span class="string">&#x27;z&#x27;</span>)&#123;<span class="comment">//与上面思路相同</span></span><br><span class="line"></span><br><span class="line">            <span class="type">int</span> h=k[q]&gt;=<span class="string">&#x27;A&#x27;</span>&amp;&amp;k[q]&lt;=<span class="string">&#x27;Z&#x27;</span>?k[q]-<span class="string">&#x27;A&#x27;</span>:k[q]-<span class="string">&#x27;a&#x27;</span>;</span><br><span class="line"></span><br><span class="line">            <span class="keyword">for</span>(<span class="type">int</span> j=<span class="number">0</span>;j&lt;h;j++)&#123;</span><br><span class="line"></span><br><span class="line">                s[i]--;</span><br><span class="line"></span><br><span class="line">                <span class="keyword">if</span>(s[i]&lt;<span class="string">&#x27;a&#x27;</span>)&#123;</span><br><span class="line"></span><br><span class="line">                    s[i]=<span class="string">&#x27;z&#x27;</span>;</span><br><span class="line"></span><br><span class="line">                &#125;</span><br><span class="line"></span><br><span class="line">            &#125;</span><br><span class="line"></span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        q++;<span class="comment">//指针指向下一位</span></span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span>(q==k.<span class="built_in">size</span>())&#123;<span class="comment">//特判，使指针回到开头</span></span><br><span class="line"></span><br><span class="line">            q=<span class="number">0</span>;</span><br><span class="line"></span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    cout&lt;&lt;s;<span class="comment">//输出</span></span><br><span class="line"></span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line"></span><br><span class="line">&#125; </span><br></pre></td></tr></table></figure>

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